Question

How to calculate this? `int_(-1)^1(1+2x^2015)e^(-absx)dx`.

Answer 1

`2(e-1)/e`

Explanation:

`int_(-1)^1(1+2x^2015)e^(-absx)dx = int_-1^1e^-abs(x)dx + 2int_-1^1x^2015 e^-abs(x)dx=int_-1^1 e^-abs(x) dx = 2int_0^1e^-x dx= 2(e-1)/e`

NOTE:

As @Steve pointed out, `x^2015 e^-abs(x)` is an odd function so `int_-a^ax^2015 e^-abs(x)dx = 0`